The kilogram used to be defined by a specific chunk of platinum-iridium.
But now it’s defined using the second and the Plank constant, somehow.
Assuming you already have a very accurate measurement of the second, and the Plank constant, how do you combine those two things to get the kilogram?
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You can put a mass on a balance, and it will tip to that side. There are a couple of ways you could pull it back level. One way is to put an equal mass on the other side, so the force of gravity is equal on both sides. Or you could put some other kind of force on the other side. What if we used an electromagnet to pull it back to level? That’s what the watt (Kibble) balance essentially is.
So they carefully control the number of windings, thickness of wire, length of coil… Whatever needs to be controlled so that the only variables are the voltage and current running through the coil. Current is measured in amps which is equivalent to coulombs per second (we know the charge on an electron, so if we count the number of electrons passing per second, we’re measuring electric current). And volts is equivalent to joules per coulomb (again if we put an electron in a voltage field, the electron will want to move from negative to positive, that energy given to each electron to move is the measure of how strong the field is). If you multiply volts and amps together, you get watts. Notice that coulombs cancels out and you’re left with joules per second, and watts are equivalent to joules per second.
Now, a joule is the amount of energy it takes to lift a 1 newton object by 1 meter. So Joules are equivalent to newtons*meter. And with one more step we can break newton’s down into the core, SI units. A newton is a measure of force. From Isaac Newton, we learned that it’s the force required to accelerate a 1kg mass by 1m/s². And so a newton is equivalent to kg*m/s².
Let’s throw it all together. Watts are equivalent to J/s. Joules are equivalent to N*m. And newtons are equivalent to kg*m/s². Replace everything to get to the base, SI units and we have 1 kg*m²/s³ = 1W of power. Crazy right? If we can base meters and seconds off fundamental physics constants, we can turn around and define the kg based on the same units. Planck’s constant not being a unit is more or less there to make the math look nicer as I understand. The same way we use Avogadro’s number so we don’t have to talk about sextillions of things. (Note, Planck’s constant does *have* units, but it itself is not a unit)
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